For the first scenario with ordinal categorical outcome, we
generated data as above under the null hypothesis, so with
\(\beta = \beta _0=0\) , and \(\beta =\beta _A = \log (1.5)\) ,
corresponding to the alternative for which TESICO was powered
(80% at the final analysis with \(n=602\) )[1]}, and
\(\mbox{H}_A\!\!: \beta _0 > 0\) . Here, \(\widehat{\beta }_{\mathcal {T}_F}(t)\)  is the
ML estimator for \(\beta \)  in (REF ) obtained
using the R function polr in the MASS package[2]}. Following
Tsiatis et al.[1]}, to simplify implementation, we
constructed \(\widehat{\beta }_{IPW}(t)\) , \(\widehat{\beta }_{AIPW1}(t)\) , and
\(\widehat{\beta }_{AIPW2}(t)\)  using the estimating function
(REF ) with
\(\mathcal {D}(A) = D^T(A; \alpha ,\beta ) V^{-1}_{ind}(A; \alpha ,\beta )\) ,
where \( V_{ind}(A; \alpha ,\beta )\)  is chosen according to the
“working independence” assumption, so that with full data at
the final analysis, \(\widehat{\beta }_{\mathcal {T}_F}(t_{end})\)  and
\(\widehat{\beta }_{IPW}(t_{end})\)  are not identical. As shown by
Tsiatis et al.[1]} and borne out in the simulations
below, the efficiency loss for \(\widehat{\beta }_{IPW}(t_{end})\) 
relative to \(\widehat{\beta }_{\mathcal {T}_F}(t_{end})\)  is negligible.
